FBX exporter with a material overwrite with python
So I made a work around. The key was saving the original material, assigning the overwrite material, then reapplying the original. You will need to change the settings for the fbx export click here for its structure.

 fbxs = [ ob for ob in bpy.context.selected_objects]
 bpy.ops.object.select_all(action='DESELECT')

    for ob in fbxs:
         ob.select_set(True)
         mat = bpy.data.materials['Overwrite']
         original_mat = ob.data.materials
         ob.data.materials[0] = mat

         bpy.ops.export_scene.fbx(...)

         ob.data.materials[0] = original_mat
         bpy.ops.object.select_all(action='DESELECT')